{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "minor-myanmar",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "median-indonesian",
   "metadata": {},
   "outputs": [],
   "source": [
    "def JosephsonSolver(V,period = np.pi*2,N=1000):\n",
    "    X = np.linspace(0,period,N)\n",
    "    dx = period/N\n",
    "    P = -np.diag(np.ones(N))+np.diag(np.ones(N-1),1)\n",
    "    P+=P.T\n",
    "    P[0,-1],P[-1,0]=1,1 # you should use periodic boundary\n",
    "    M = -4/dx**2 * P + np.diag(V(X))\n",
    "    return np.diff(np.sort(LA.eigvalsh(M))[0:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "western-equality",
   "metadata": {},
   "source": [
    "$$\n",
    "H = 4E_C n^2 -2E_J |\\cos{\\phi_e}|\\cos{\\phi}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "declared-necessity",
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM = 1000\n",
    "phie = np.linspace(-np.pi,np.pi,NUM)\n",
    "Ej = 50\n",
    "res = np.zeros((NUM,2))\n",
    "for i in range(len(phie)):\n",
    "    res[i] = JosephsonSolver(lambda x:-2*Ej*np.abs(np.cos(phie[i]))*np.cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "faced-baseline",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$H = 4E_C n^2 -2E_J |\\\\cos{\\\\phi_e}|\\\\cos{\\\\phi}$')"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "ax.plot(phie,res)\n",
    "title=r\"$H = 4E_C n^2 -2E_J |\\cos{\\phi_e}|\\cos{\\phi}$\"\n",
    "ax.set_title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "obvious-abuse",
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM = 100\n",
    "phie = np.linspace(-np.pi*2,np.pi*2,NUM) # note in paper, it is \\Phi\n",
    "gamma,Ej,El =2.5,50,1\n",
    "res = np.zeros((NUM,2))\n",
    "for i in range(len(res)):\n",
    "    res[i] = JosephsonSolver(lambda phi:-Ej*np.cos(2*phi+phie[i])-2*gamma*Ej*np.cos(phi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "operational-spouse",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$H = 4E_C n^2 -E_J\\\\cos{(2\\\\phi+\\\\phi_e)}-2\\\\gamma E_J\\\\cos{\\\\phi}$')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "ax.plot(phie,res)\n",
    "title=r\"$H = 4E_C n^2 -E_J\\cos{(2\\phi+\\phi_e)}-2\\gamma E_J\\cos{\\phi}$\"\n",
    "ax.set_title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "intense-logic",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:mysci]",
   "language": "python",
   "name": "conda-env-mysci-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
